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                    1.1 策略模式
            
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                    1.8 适配器模式
            
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                    1.9 装饰者模式
            
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                    1.10 享元模式
            
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                    1.11 代理模式
            
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                    1.12 中间件模式
            
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                    2.1 长连接
            
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                    2.2 MQ
            
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                    3.1.7 性能调优
            
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                    3.1.8 其他: Node爬虫
            
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                    3.1.9 其他: Node编写Mapreduce
            
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                    3.2 C/C++
            
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                    3.2.1 面向对象
            
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                    3.2.2 进程通信
            
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                    3.2.3 线程管理
            
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                    3.2.4 内存管理
            
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                    3.2.5 网络编程
            
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                    3.2.6 构建工具
            
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                    3.2.7 其他: 线程池
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    

            </ul>
            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4" data-path="../engineering/ci_deplopment/">
            
                <a href="../engineering/ci_deplopment/">
            
                    
                    三 搭建部署
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.1" data-path="../engineering/ci_deplopment/test.html">
            
                <a href="../engineering/ci_deplopment/test.html">
            
                    
                    3.1 测试
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.1.1" data-path="../engineering/ci_deplopment/test/unit_testing.html">
            
                <a href="../engineering/ci_deplopment/test/unit_testing.html">
            
                    
                    3.1.1 单元测试
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.1.2" data-path="../engineering/ci_deplopment/test/stress_testing.html">
            
                <a href="../engineering/ci_deplopment/test/stress_testing.html">
            
                    
                    3.1.2 压力测试
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4.2" data-path="../engineering/ci_deplopment/ci_readme.html">
            
                <a href="../engineering/ci_deplopment/ci_readme.html">
            
                    
                    3.2 集成
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.2.1" data-path="../engineering/ci_deplopment/ci/gitlab_ci.html">
            
                <a href="../engineering/ci_deplopment/ci/gitlab_ci.html">
            
                    
                    3.2.1 GitLab CI
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.2.2" data-path="../engineering/ci_deplopment/ci/spinnaker.html">
            
                <a href="../engineering/ci_deplopment/ci/spinnaker.html">
            
                    
                    3.2.2 Spinnaker
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4.3" data-path="../engineering/ci_deplopment/build.html">
            
                <a href="../engineering/ci_deplopment/build.html">
            
                    
                    3.3 部署
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.3.1" data-path="../engineering/ci_deplopment/k8s/k8s.html">
            
                <a href="../engineering/ci_deplopment/k8s/k8s.html">
            
                    
                    3.3.1 k8s
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.3.2" data-path="../engineering/ci_deplopment/rancher/rancher.html">
            
                <a href="../engineering/ci_deplopment/rancher/rancher.html">
            
                    
                    3.3.2 rancher
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.3.3" data-path="../engineering/ci_deplopment/swarm/swarm.html">
            
                <a href="../engineering/ci_deplopment/swarm/swarm.html">
            
                    
                    3.3.3 swarm
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4.4" data-path="../engineering/ci_deplopment/maintenance.html">
            
                <a href="../engineering/ci_deplopment/maintenance.html">
            
                    
                    3.4 监控
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.4.1" data-path="../engineering/ci_deplopment/monitor.html">
            
                <a href="../engineering/ci_deplopment/monitor.html">
            
                    
                    3.4.1 容器监控
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.4.2" data-path="../engineering/ci_deplopment/trace.html">
            
                <a href="../engineering/ci_deplopment/trace.html">
            
                    
                    3.4.2 系统监控
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.4.4.3" data-path="../engineering/ci_deplopment/app1.md">
            
                <span>
            
                    
                    3.4.2 应用监控
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4.5" data-path="../engineering/ha/ha.html">
            
                <a href="../engineering/ha/ha.html">
            
                    
                    3.5 高可用
            
                </a>
            

            
            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.5.1" data-path="../engineering/ha/client.html">
            
                <a href="../engineering/ha/client.html">
            
                    
                    3.5.1 接入层高可用
            
                </a>
            

            
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        <li class="chapter " data-level="1.4.5.2" data-path="../engineering/ha/service.html">
            
                <a href="../engineering/ha/service.html">
            
                    
                    3.5.2 服务层高可用
            
                </a>
            

            
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        <li class="chapter " data-level="1.4.5.3" data-path="../engineering/ha/share.html">
            
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                    3.5.3 存储层高可用
            
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            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.4.6" data-path="../engineering/ci_deplopment/hc/hc.html">
            
                <a href="../engineering/ci_deplopment/hc/hc.html">
            
                    
                    3.6 高并发
            
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            <ul class="articles">
                
    
        <li class="chapter " data-level="1.4.6.1" data-path="../engineering/ci_deplopment/hc/dns.html">
            
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                    3.6.1 基于DNS的负载均衡
            
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        <li class="chapter " data-level="1.4.6.2" data-path="../engineering/ci_deplopment/hc/lvs.html">
            
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                    3.6.2 基于Lvs的负载均衡
            
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        <li class="chapter " data-level="1.4.6.3" data-path="../engineering/ci_deplopment/hc/haproxy.html">
            
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                    3.6.3 基于haproxy的负载均衡
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    

            </ul>
            
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        <li class="chapter " data-level="1.5" >
            
                <span>
            
                    
                    四 架构模式
            
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        <li class="chapter " data-level="1.5.1" >
            
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                    1 微服务架构设计与实践
            
                </span>
            

            
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        <li class="chapter " data-level="1.5.1.1" data-path="../program/java/spring-cloud.html">
            
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                    1.1 微服务概况
            
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        <li class="chapter " data-level="1.5.1.2" data-path="../program/java/spring-eureka.html">
            
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                    1.2 服务注册及发现
            
                </a>
            

            
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        <li class="chapter " data-level="1.5.1.3" data-path="../program/java/spring-feign.html">
            
                <a href="../program/java/spring-feign.html">
            
                    
                    1.3 服务调用
            
                </a>
            

            
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        <li class="chapter " data-level="1.5.1.4" data-path="../program/java/spring-zuul.html">
            
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                    1.4 网关及负载均衡
            
                </a>
            

            
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        <li class="chapter " data-level="1.5.1.5" data-path="../program/java/spring-hystrix.html">
            
                <a href="../program/java/spring-hystrix.html">
            
                    
                    1.5 熔断、限流、扩缩容
            
                </a>
            

            
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        <li class="chapter " data-level="1.5.1.6" data-path="../program/java/spring-config.html">
            
                <a href="../program/java/spring-config.html">
            
                    
                    1.6 云配置中心
            
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        <li class="chapter " data-level="1.5.1.7" data-path="../program/java/zipkin-tracing.html">
            
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                    1.7 分布式链路追踪
            
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        <li class="chapter " data-level="1.5.1.8" data-path="../program/java/swagger.html">
            
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                    1.8 接口文档管理
            
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                    2 领域驱动模型
            
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                    2.1 领域--Domain
            
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        <li class="chapter " data-level="1.5.2.2" data-path="../domain/entity.md">
            
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                    2.2 领域实体--Entity
            
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        <li class="chapter " data-level="1.5.2.3" data-path="../domain/object.html">
            
                <a href="../domain/object.html">
            
                    
                    2.3 值对象--Value Object
            
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        <li class="chapter " data-level="1.5.2.4" data-path="../domain/aggregate.html">
            
                <a href="../domain/aggregate.html">
            
                    
                    2.4 聚合--Aggregate
            
                </a>
            

            
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        <li class="chapter " data-level="1.5.2.5" data-path="../domain/service.html">
            
                <a href="../domain/service.html">
            
                    
                    2.5 服务--Services
            
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        <li class="chapter " data-level="1.5.2.6" data-path="../domain/event.html">
            
                <a href="../domain/event.html">
            
                    
                    2.6 领域事件--Event
            
                </a>
            

            
        </li>
    
        <li class="chapter " data-level="1.5.2.7" data-path="../domain/framework.html">
            
                <a href="../domain/framework.html">
            
                    
                    2.7 几种常见的DDD架构
            
                </a>
            

            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.5.3" >
            
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                    3 架构技术的演化与趋势
            
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            <ul class="articles">
                
    
        <li class="chapter " data-level="1.5.3.1" >
            
                <span>
            
                    
                    3.1 架构技术的发展历史及现状
            
                </span>
            

            
        </li>
    
        <li class="chapter " data-level="1.5.3.2" >
            
                <span>
            
                    
                    3.2 Serverless无服务架构概念
            
                </span>
            

            
        </li>
    
        <li class="chapter " data-level="1.5.3.3" >
            
                <span>
            
                    
                    3.3 ServerMesh网格服务概念
            
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        </li>
    

            </ul>
            
        </li>
    

            </ul>
            
        </li>
    
        <li class="chapter " data-level="1.6" >
            
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                    五 其他
            
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            <ul class="articles">
                
    
        <li class="chapter " data-level="1.6.1" data-path="../story/talk.html">
            
                <a href="../story/talk.html">
            
                    
                    5.1 小伙子,放松!
            
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                                <h3 id="&#x4E00;&#x3001;&#x7B80;&#x4ECB;">&#x4E00;&#x3001;&#x7B80;&#x4ECB;</h3>
<p>&#xA0;&#xA0;&#xA0;&#xA0;&#x5728;&#x4E00;&#x4E9B;&#x5B9E;&#x9645;&#x7684;&#x51B3;&#x7B56;&#x8FC7;&#x7A0B;&#x4E2D;&#xFF0C;&#x901A;&#x5E38;&#x4F1A;&#x8BBE;&#x5B9A;&#x591A;&#x4E2A;&#x76EE;&#x6807;&#xFF0C;&#x4E3A;&#x89E3;&#x51B3;&#x8FD9;&#x7C7B;&#x95EE;&#x9898;&#x9700;&#x8981;&#x5F15;&#x5165;&#x76EE;&#x6807;&#x89C4;&#x5212;&#xFF0C;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x76F8;&#x6BD4;&#x7EBF;&#x6027;&#x89C4;&#x5212;&#x3001;&#x6574;&#x6570;&#x89C4;&#x5212;&#x3001;&#x975E;&#x7EBF;&#x6027;&#x89C4;&#x5212;&#x7B49;&#x5355;&#x4E00;&#x76EE;&#x6807;&#x6A21;&#x578B;&#x66F4;&#x63A5;&#x8FD1;&#x5B9E;&#x9645;&#x51B3;&#x7B56;&#x3002;&#x5982;&#x5728;&#x516C;&#x53F8;&#x6295;&#x653E;&#x5E7F;&#x544A;&#x65F6;&#xFF0C;&#x8FD0;&#x8425;&#x51B3;&#x7B56;&#x8005;&#x901A;&#x5E38;&#x5E0C;&#x671B;&#x5728;&#x5404;&#x4E2A;&#x6E20;&#x9053;&#x7684;&#x6295;&#x653E;&#x91CF;&#x3001;&#x5BFC;&#x5165;&#x6D41;&#x91CF;&#x3001;&#x65E5;&#x6D3B;&#x3001;&#x6EE1;&#x610F;&#x5EA6;&#x7B49;&#x90FD;&#x5206;&#x522B;&#x5927;&#x4E8E;&#x5BF9;&#x5E94;&#x671F;&#x671B;&#x503C;&#xFF0C;&#x8FD9;&#x7C7B;&#x5B58;&#x5728;&#x4F18;&#x5148;&#x7EA7;&#x7684;&#x591A;&#x76EE;&#x6807;&#x6A21;&#x578B;&#x5219;&#x53EF;&#x5212;&#x5F52;&#x4E3A;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x7684;&#x6C42;&#x89E3;&#x8303;&#x7574;&#x3002;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x5305;&#x62EC;&#x7EBF;&#x6027;&#x3001;&#x975E;&#x7EBF;&#x6027;&#xFF0C;&#x672C;&#x8282;&#x4E3B;&#x8981;&#x5206;&#x4EAB;&#x7EBF;&#x6027;&#x76EE;&#x6807;&#x89C4;&#x5212;&#xFF0C;&#x5176;&#x6570;&#x5B66;&#x6A21;&#x578B;&#x5982;&#x4E0B;:</p>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>Z</mi><mo>=</mo><msubsup><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><mi>p</mi><mi>i</mi><mo>[</mo><msubsup><mo>&#x2211;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></msubsup><mo>(</mo><msubsup><mi>w</mi><mrow><mi>i</mi><mi>k</mi></mrow><mo>&#x2212;</mo></msubsup><msubsup><mi>d</mi><mi>k</mi><mo>&#x2212;</mo></msubsup><mo>+</mo><msubsup><mi>w</mi><mrow><mi>i</mi><mi>k</mi></mrow><mo>+</mo></msubsup><msubsup><mi>d</mi><mi>k</mi><mo>+</mo></msubsup><mo>)</mo><mo>]</mo></mrow><annotation encoding="application/x-tex">
minZ = \sum_{i=1}^kpi[\sum_{k=1}^m(w_{ik}^-d_k^- + w_{ik}^+d_k^+)]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.8361130000000003em;"></span><span class="strut bottom" style="height:3.1382260000000004em;vertical-align:-1.302113em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">m</span><span class="mord mathit">i</span><span class="mord mathit">n</span><span class="mord mathit" style="margin-right:0.07153em;">Z</span><span class="mrel">=</span><span class="mop op-limits"><span class="vlist"><span style="top:1.1776689999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.000005000000000143778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-1.2500050000000003em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord mathit">p</span><span class="mord mathit">i</span><span class="mopen">[</span><span class="mop op-limits"><span class="vlist"><span style="top:1.202113em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.000005000000000032756em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-1.250005em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">m</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.2914389999999999em;margin-left:-0.02691em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.2914389999999999em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist"><span style="top:0.2914389999999999em;margin-left:-0.02691em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.2914389999999999em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">)</span><span class="mclose">]</span></span></span></span></span> </p>
<center>
<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">{</mo><mtable><mtr><mtd><mrow><msubsup><mo>&#x2211;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>a</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub><msub><mi>x</mi><mi>j</mi></msub><mo>&#x2264;</mo><mo>(</mo><mo>=</mo><mo>&#x2265;</mo><mo>)</mo><msub><mi>b</mi><mi>j</mi></msub><mo separator="true">,</mo><mi>t</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>L</mi></mrow></mtd></mtr><mtr><mtd><mrow><msubsup><mo>&#x2211;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></msubsup><msub><mi>c</mi><mrow><mi>k</mi><mi>j</mi></mrow></msub><msub><mi>x</mi><mi>j</mi></msub><mo>+</mo><msubsup><mi>d</mi><mi>j</mi><mo>&#x2212;</mo></msubsup><mo>&#x2212;</mo><msubsup><mi>d</mi><mi>j</mi><mo>+</mo></msubsup><mo>=</mo><msub><mi>g</mi><mi>k</mi></msub><mo separator="true">,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>m</mi></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>&gt;</mo><mn>0</mn><mo separator="true">,</mo><msubsup><mi>d</mi><mi>k</mi><mi>j</mi></msubsup><mo>&gt;</mo><mn>0</mn><mo>(</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>n</mi><mo separator="true">,</mo><mi>k</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>m</mi><mo>)</mo></mrow></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex"> \left\{
\begin{aligned}
\sum_{j=1}^na_{kj}x_j \le(=\ge)b_j, t=1,2,...,L\\
\sum_{j=1}^mc_{kj}x_j + d_j^- - d_j^+ = g_k,i=1,2,...,m \\
x_j &gt; 0, d_k^j&gt;0(j=1,...,n, k = 1,...,m)
\end{aligned}
\right.
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:2.177404em;"></span><span class="strut bottom" style="height:3.8548080000000002em;vertical-align:-1.677404em;"></span><span class="base textstyle uncramped"><span class="minner textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.65001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A9;</span></span></span><span style="top:-0.000010000000000065512em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A8;</span></span></span><span style="top:-1.15002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A7;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist"><span style="top:-1.337404em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">a</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&#x2264;</span><span class="mopen">(</span><span class="mrel">=</span><span class="mrel">&#x2265;</span><span class="mclose">)</span><span class="mord"><span class="mord mathit">b</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathit">t</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">L</span></span></span><span style="top:-0.06128599999999995em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">m</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">c</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.276864em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.276864em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathit">i</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">m</span></span></span><span style="top:1.3174039999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&gt;</span><span class="mord mathrm">0</span><span class="mpunct">,</span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.3013079999999999em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span style="top:-0.480908em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">&gt;</span><span class="mord mathrm">0</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.05724em;">j</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">n</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">m</span><span class="mclose">)</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span></span></span></span>
</center>

<p>&#x5176;&#x4E2D;:</p>
<pre><code>1&#x3001;minZ&#x4E3A;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x7684;&#x76EE;&#x6807;&#x884C;&#x6570;&#xFF0C;&#x5728;&#x6A21;&#x578B;&#x77E9;&#x9635;&#x4E2D;&#xFF0C;&#x7B2C;&#x4E00;&#x884C;&#x4E3A;&#x7EDD;&#x5BF9;&#x7EA6;&#x675F;&#xFF0C;&#x7B2C;&#x4E8C;&#x884C;&#x4E3A;&#x76EE;&#x6807;&#x7EA6;&#x675F;
2&#x3001;d&#x4E3A;&#x6B63;&#x8D1F;&#x504F;&#x5DEE;&#x53D8;&#x91CF;&#xFF0C;&#x4EE3;&#x8868;&#x504F;&#x79FB;&#x7406;&#x60F3;&#x503C;&#x5F97;&#x65B9;&#x5411;&#xFF0C;+&#x4E3A;&#x7406;&#x60F3;&#x503C;&#x52A0;d&#xFF0C;-&#x4E3A;&#x7406;&#x60F3;&#x503C;&#x51CF;d
3&#x3001;&#x7B2C;&#x4E09;&#x884C;&#x4E3A;&#x7EA6;&#x675F;&#x53D8;&#x91CF;&#x53CA;&#x7EDD;&#x5BF9;&#x53D8;&#x91CF;&#x5B9A;&#x4E49;&#x57DF;
</code></pre><hr>
<h3 id="&#x4E8C;&#x3001;&#x5E94;&#x7528;">&#x4E8C;&#x3001;&#x5E94;&#x7528;</h3>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mi>Z</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub><mo>(</mo><msubsup><mi>d</mi><mn>1</mn><mo>&#x2212;</mo></msubsup><mo>+</mo><mn>2</mn><msubsup><mi>d</mi><mn>2</mn><mo>&#x2212;</mo></msubsup><mo>)</mo><mo>+</mo><msub><mi>P</mi><mn>2</mn></msub><msubsup><mi>d</mi><mn>1</mn><mo>+</mo></msubsup><mo>+</mo><msub><mi>P</mi><mn>3</mn></msub><msubsup><mi>d</mi><mn>3</mn><mo>+</mo></msubsup><mo>+</mo><msub><mi>P</mi><mn>4</mn></msub><msubsup><mi>d</mi><mn>4</mn><mo>+</mo></msubsup></mrow><annotation encoding="application/x-tex">
minZ = P_1(d_1^- + 2d_2^- ) + P_2d_1^+ + P_3d_3^+ + P_4d_4^+
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8213309999999999em;"></span><span class="strut bottom" style="height:1.07777em;vertical-align:-0.256439em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord mathit">m</span><span class="mord mathit">i</span><span class="mord mathit">n</span><span class="mord mathit" style="margin-right:0.07153em;">Z</span><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.256439em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.256439em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">)</span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.256439em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.256439em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.13889em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.256439em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span></span></span><span style="top:-0.4129999999999999em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span></span> </p>
<center>
<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mrow><mo fence="true">{</mo><mtable><mtr><mtd><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>1</mn><msub><mi>x</mi><mrow><mn>1</mn><mn>1</mn></mrow></msub><mtext>&#xA0;</mtext><mo>+</mo><mtext>&#xA0;</mtext><mn>7</mn><mi mathvariant="normal">.</mi><mn>2</mn><mn>6</mn><msub><mi>x</mi><mrow><mn>1</mn><mn>2</mn></mrow></msub><mo>+</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>1</mn><mo>&#x2212;</mo></msubsup><mo>&#x2212;</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>1</mn><mo>+</mo></msubsup><mo>=</mo><mtext>&#xA0;</mtext><mn>1</mn><mn>2</mn><mi mathvariant="normal">.</mi><mn>3</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>2</mn><mn>4</mn><msub><mi>x</mi><mrow><mn>2</mn><mn>1</mn></mrow></msub><mtext>&#xA0;</mtext><mo>+</mo><mtext>&#xA0;</mtext><mn>0</mn><mi mathvariant="normal">.</mi><mn>4</mn><msub><mi>x</mi><mrow><mn>2</mn><mn>2</mn></mrow></msub><mo>+</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>2</mn><mo>&#x2212;</mo></msubsup><mo>&#x2212;</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>2</mn><mo>+</mo></msubsup><mo>=</mo><mtext>&#xA0;</mtext><mn>1</mn><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>1</mn><mi mathvariant="normal">.</mi><mn>6</mn><mn>8</mn><msub><mi>x</mi><mrow><mn>3</mn><mn>1</mn></mrow></msub><mtext>&#xA0;</mtext><mo>+</mo><mtext>&#xA0;</mtext><mn>0</mn><mi mathvariant="normal">.</mi><mn>1</mn><msub><mi>x</mi><mrow><mn>3</mn><mn>2</mn></mrow></msub><mo>+</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>3</mn><mo>&#x2212;</mo></msubsup><mo>&#x2212;</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>3</mn><mo>+</mo></msubsup><mo>=</mo><mtext>&#xA0;</mtext><mn>1</mn><mn>4</mn></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>6</mn><mn>8</mn><msub><mi>x</mi><mrow><mn>4</mn><mn>1</mn></mrow></msub><mtext>&#xA0;</mtext><mo>+</mo><mtext>&#xA0;</mtext><mn>0</mn><mi mathvariant="normal">.</mi><mn>2</mn><msub><mi>x</mi><mrow><mn>4</mn><mn>2</mn></mrow></msub><mo>+</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>4</mn><mo>&#x2212;</mo></msubsup><mo>&#x2212;</mo><mtext>&#xA0;</mtext><msubsup><mi>d</mi><mn>4</mn><mo>+</mo></msubsup><mo>=</mo><mtext>&#xA0;</mtext><mn>1</mn><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow></mrow></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex"> \left\{
\begin{aligned}
0.1x_{11}\ +\  7.26x_{12} +\ d_1^- -\ d_1^+ = \ 12.3 \\
0.24x_{21}\ +\ 0.4x_{22} +\ d_2^- -\ d_2^+ =\ 14 \\
1.68x_{31}\ +\ 0.1x_{32} +\ d_3^- -\ d_3^+ =\ 14 \\
0.68x_{41}\ +\ 0.2x_{42} +\ d_4^- -\ d_4^+ =\ 10 \\

\end{aligned}
\right.
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:3.2500199999999997em;"></span><span class="strut bottom" style="height:6.00004em;vertical-align:-2.75002em;"></span><span class="base textstyle uncramped"><span class="minner textstyle uncramped"><span class="mopen style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:1.8500100000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A9;</span></span></span><span style="top:1.8500100000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:1.55001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:1.25001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:0.95001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-0.000010000000000065512em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A8;</span></span></span><span style="top:-1.15001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-1.45001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-1.75001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-2.05001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23AA;</span></span></span><span style="top:-2.3500199999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="delimsizinginner delim-size4"><span>&#x23A7;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist"><span style="top:-2.41em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin"><span class="mspace">&#xA0;</span><span class="mbin">+</span></span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">7</span></span><span class="mord mathrm">.</span><span class="mord mathrm">2</span><span class="mord mathrm">6</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span><span class="mord mathrm mtight">2</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">1</span></span><span class="mord mathrm">2</span><span class="mord mathrm">.</span><span class="mord mathrm">3</span></span></span><span style="top:-1.2100000000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">2</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin"><span class="mspace">&#xA0;</span><span class="mbin">+</span></span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">0</span></span><span class="mord mathrm">.</span><span class="mord mathrm">4</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span><span class="mord mathrm mtight">2</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">2</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">1</span></span><span class="mord mathrm">4</span></span></span><span style="top:-0.009999999999999953em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">.</span><span class="mord mathrm">6</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin"><span class="mspace">&#xA0;</span><span class="mbin">+</span></span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">0</span></span><span class="mord mathrm">.</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span><span class="mord mathrm mtight">2</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">3</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">1</span></span><span class="mord mathrm">4</span></span></span><span style="top:1.1900000000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">6</span><span class="mord mathrm">8</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span><span class="mord mathrm mtight">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin"><span class="mspace">&#xA0;</span><span class="mbin">+</span></span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">0</span></span><span class="mord mathrm">.</span><span class="mord mathrm">2</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span><span class="mord mathrm mtight">2</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">+</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">&#x2212;</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x2212;</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathit">d</span><span class="msupsub"><span class="vlist"><span style="top:0.266308em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">4</span></span></span><span style="top:-0.403131em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mbin mtight">+</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mrel">=</span><span class="mord mathrm"><span class="mspace">&#xA0;</span><span class="mord mathrm">1</span></span><span class="mord mathrm">0</span></span></span><span style="top:2.3900000000000006em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="mord textstyle uncramped"></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span></span></span></span>
</center>

<h4 id="&#x4EE5;&#x4E0A;&#x4E3A;&#x4E00;&#x4E2A;&#x7EBF;&#x6027;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x6A21;&#x578B;&#xFF0C;&#x901A;&#x8FC7;goalprog&#x6C42;&#x89E3;&#xFF1A;">&#x4EE5;&#x4E0A;&#x4E3A;&#x4E00;&#x4E2A;&#x7EBF;&#x6027;&#x76EE;&#x6807;&#x89C4;&#x5212;&#x6A21;&#x578B;&#xFF0C;&#x901A;&#x8FC7;goalprog&#x6C42;&#x89E3;&#xFF1A;</h4>
<pre><code class="lang-R"><span class="hljs-keyword">library</span>(goalprog)
<span class="hljs-keyword">library</span>(lpSolve)

coefficients &lt;- matrix(
  c(<span class="hljs-number">0.1</span>, <span class="hljs-number">0.24</span>, <span class="hljs-number">1.68</span>, <span class="hljs-number">0.68</span>, <span class="hljs-number">7.26</span>, <span class="hljs-number">0.4</span>, <span class="hljs-number">0.1</span>, <span class="hljs-number">0.2</span>), 
  <span class="hljs-number">4</span>
)

targets &lt;- c(<span class="hljs-number">12.3</span>, <span class="hljs-number">14</span>, <span class="hljs-number">14</span>, <span class="hljs-number">10</span>)

achievements &lt;- data.frame(
  objective = <span class="hljs-number">1</span>:<span class="hljs-number">4</span>,
  priority = c(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>),
  p = c(<span class="hljs-number">1</span>, <span class="hljs-number">0</span>, <span class="hljs-number">1</span>, <span class="hljs-number">1</span>),
  n = c(<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>)
)

soln &lt;- llgp(coefficients, targets, achievements)

soln$converged

soln$out
</code></pre>
<h4 id="&#x7EC8;&#x7AEF;&#x6253;&#x5370;">&#x7EC8;&#x7AEF;&#x6253;&#x5370;:</h4>
<pre><code class="lang-R">Dreamboad:dreamboad helloworld$ Rscript  optimization_se/MOP.R
&#x8F7D;&#x5165;&#x9700;&#x8981;&#x7684;&#x7A0B;&#x8F91;&#x5305;&#xFF1A;lpSolve
[<span class="hljs-number">1</span>] <span class="hljs-literal">TRUE</span>

Decision variables
                X
X1   <span class="hljs-number">5.681391e+01</span>
X2   <span class="hljs-number">9.116541e-01</span>

Summary of objectives
        Objective           Over          Under         Target
G1   <span class="hljs-number">1.230000e+01</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">1.230000e+01</span>
G2   <span class="hljs-number">1.400000e+01</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">1.400000e+01</span>
G3   <span class="hljs-number">9.553853e+01</span>   <span class="hljs-number">8.153853e+01</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">1.400000e+01</span>
G4   <span class="hljs-number">3.881579e+01</span>   <span class="hljs-number">2.881579e+01</span>   <span class="hljs-number">0.000000e+00</span>   <span class="hljs-number">1.000000e+01</span>

Achievement <span class="hljs-keyword">function</span>
                A
P1   <span class="hljs-number">0.000000e+00</span>
P2   <span class="hljs-number">0.000000e+00</span>
P3   <span class="hljs-number">8.153853e+01</span>
P4   <span class="hljs-number">2.881579e+01</span>
</code></pre>
<h4 id="&#x5176;&#x4E2D;&#x53C2;&#x6570;">&#x5176;&#x4E2D;&#x53C2;&#x6570;:</h4>
<pre><code class="lang-R">coefficients: &#x6A21;&#x578B;&#x77E9;&#x9635;&#x7CFB;&#x6570;
objective:  &#x7B2C;&#x51E0;&#x5BF9;&#x504F;&#x5DEE;&#x53D8;&#x91CF;
priority:  &#x4F18;&#x5148;&#x56E0;&#x5B50;
p:  &#x6B63;&#x504F;&#x91CF;&#x7CFB;&#x6570;
n:  &#x8D1F;&#x504F;&#x91CF;&#x7CFB;&#x6570;
</code></pre>
<hr>
<h3 id="&#x4E09;&#x3001;&#x53C2;&#x8003;">&#x4E09;&#x3001;&#x53C2;&#x8003;</h3>
<ul>
<li><a href="https://cran.r-project.org/web/packages/goalprog/goalprog.pdf" target="_blank">1&#x3001;goalprog&#x6587;&#x6863;</a> </li>
</ul>
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